Using the method of homogenization to calculate the effective diffusivity of the stratum corneum

The stratum corneum is the outermost layer of the skin, which acts as a barrier membrane against the penetration of molecules into and out of the body. It has a biphasic structure consisting of keratinized cells – the corneocytes – that are embedded in an ordered lipid matrix. Transport of molecules through the stratum corneum has direct analogies to the classic problem of diffusion of solutes across a composite membrane. The macroscopic transport properties of the stratum corneum are functions of its microscopic structure and the transport properties of the corneocytes and the lipid matrix. We obtain the macroscopic diffusion coefficients of the stratum corneum through homogenization of the diffusion equation using the method of asymptotic expansions. Unlike previous studies that were limited to considering the 2D cross-section of the stratum corneum, homogenization allows the calculation of the 3D effective diffusivity tensor. Assuming the corneocytes to be impermeable, we studied the effects that different geometric arrangements of the corneocytes within the lipid matrix have on the continuum diffusion coefficients. The results indicate that the thin elongated shape of the corneocytes is ideally suited to lowering the effective diffusivity of the stratum corneum.